\section{Conclusions and Future Work}

We have presented a novel approach for skilled team formation, based on finding dense subgraphs of collaborative nodes. On the theoretical front, we have shown constant factor approximation algorithms to our problem definition. On the practical side, we shown several heuristic improvements to our main provable algorithm, and compared it to the previous approach based on identifying small diameter subgraphs. Our experimental results show that the densest subgraph approach significantly outperforms the previous techniques on multiple different measures of collaborative compatibility of a team. 

Several questions remain open. The main algorithm we have presented as well as the provable algorithms from Lappas et al.~\cite{LLT}, in the worst case, have a time complexity cubic in the number of nodes. A question is to find better linear time algorithms. For the density objective, there is a 6-approximation linear-time algorithm, and a specific question is whether this can be modified to obtain a linear time 3-approximation. Another concern with some of these algorithms is that they sometimes result in disconnected components.  While our heuristics address this issue, a more robust approach would be nice.  Another direction for future work is to see how different techniques perform when the number of skilled involved in the graph is larger. 

Finally, team formation definitions can be extended along many dimensions. For example, while nodes are selected into a team based on multiple skills they possess, a node's contributions eventually are limited also by time constraints. Further, there are other assets of nodes that may contribute to a team's compatibility, such as their affiliation institutes, cultural backgrounds, geographical location, personalities etc. Many of these characteristics cannot even be measured easily, and thereby make the team formation problem very complex in reality. The current formulations do not address these issues. While the current models are a good start, it would be nice to move closer to the motivating realistic scenario.

\noindent {\bf Acknowledgements.} We would like to thank anonymous reviewers for helpful comments.